Various methods and processes have been disclosed for the manufacture of spiral bevel gears or bevel gear wheels having curved tooth flanks. In one arrangement a grinding disk formed as a truncated cone is made to oscillate longitudinally along the tooth flanks, the disk trajectory being the vectoral sum of several motion components. An arrangement of this type is very complicated and does not permit the manufacture of bevel gears having large diameters. In another arrangement the bevel gear wheel is rotated around its own axis while it is oscillated about an axis perpendicular to a conical surface line thereof, the grinding tool meanwhile rotating about a fixed axis. This latter arrangement is even more unsuitable for the manufacture of large bevel gears as a result of the required acceleration of large masses, eventually resulting in a considerable loss of accuracy during operation.